> At 11:06 PM 11/1/2012, Louis Talman wrote:>> Those who succeed in mathematics today generally did well at arithmetic>> as kids. But when I grew up, great numbers of children did well at>> arithmetic. They had to, because calculators didn't exist. Very few of>> those people succeeded at algebra, let alone mathematics. There is a>> serious disconnect here.>>>> Are you sure of that? That's not the experience I had in my small-town> Iowa high school. My recollection is that everybody took it (Algebra I, I> mean) as freshman and most of the students were at least borderline> successful. It was proof-based geometry in the sophomore year where lots> of students, including college-intending students, "hit the wall".

Quite sure. My high school was fed by two junior highs. There were twoninth-grade first-year algebra sections (and none for eighth-grade) in myjunior high school, and the other was about the same size. The high schooldidn't offer that course.

There were just two sections of tenth-grade geometry in high school.

There was considerable attrition between ninth grade and my senior year.Only 121 were graduated. Of those, only 15 took trigonometry--the highestlevel of mathematics the school offered.

>>> And the ancient Greeks---who invented modern mathematics---are certainly>> a counterexample to your "natural progression". They accomplished a great>> deal without beginning with the algorithms we ask kids to study today.>> Indeed, it's likely that they weren't very good at arithmetic at all. So>> their "progression", if there was such a thing, was entirely different from>> the one you think you've identified.>>>> And what percentage of the general population ancient Greeks are you> talking about here? I do believe that select subset would eat modern> mathematics for lunch but the ancient Greek equivalent of an ordinary> engineering student at your campus?>

The percentage was high enough to support the famous line above the door toPlato's academy.

>> This last example suggests very strongly that arithmetic, while it may be>> *an* entry into mathematics, is not the *only* entry. Your "natural>> progression" completely ignores a significant possibility: The primacy of>> arithmetic is simply an artifact of a curriculum that denies entry to those>> who haven't acquired proficiency at arithmetic. (A curriculum, moreover,>> that's now strongly distorted by the effects of fifty years of>> standardized, multiple-guess, truth-or-consequences, mis-matching tests.)>>>> One of my old favorites for denying reality: Need improvement? Change> the curriculum and pedagogy. Need to prove that you have achieved your> goal? Change the assessments.>

That's hardly relevant to the points I raised. Especially in view of thefact that the assessments have changed the curriculum.

>> My old mandate remains appropriate, "Dance with the guy what brung ya.">> On the other hand, what's sauce for the goose is sauce for the gander.

-- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver